Asymptotic Stability Region of Slotted Aloha

Bordenave, Charles; McDonald, David; Proutière, Alexandre

doi:10.1109/tit.2012.2201333

Cited by 47 publications

(33 citation statements)

References 28 publications

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“…The proof here extends the proof of [97] by incorporating the physical-layer effect of compute-andforward. The main steps of the proof are the following.…”

Section: Appendix Bmentioning

confidence: 58%

An algebraic approach to physical-layer network coding

Feng

Silva

Kschischang

2010

2010 IEEE International Symposium on Information Theory

132

202

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This dissertation studies a family of the state-of-the-art PNC schemes called compute-and-forward (C&F). C&F was originally proposed and studied from an information-theoretic perspective. As such, it typically relies on several strong assumptions: very long block length, almost unbounded complexity, perfect channel state information, and no decoding errors at the relays; its benefit is often analyzed for simple network configurations. The aim of this dissertation is two-fold: first, to relax the above assumptions while preserving the performance of C&F, and second, to understand the benefit of C&F in more realistic network scenarios, such as random-access wireless networks.There are four main results in this dissertation. First, an algebraic framework is developed, which establishes a direct connection between C&F and module theory. This connection allows us to systematically design lattice codes for C&F with controlled block length and complexity. In particular, explicit design criteria are derived, concrete design examples are provided, and it is shown that nominal coding gains from 3 to 7.5 dB can be obtained with relatively short block length and reasonable decoding complexity. Second, a new C&F scheme is proposed, which, unlike conventional C&F schemes, does not require any channel state information (CSI). It is shown that this CSI-free scheme achieves, for a certain class of lattice codes, almost the same throughput as its CSI-enabled counterpart. Third, an end-to-end error control mechanism is designed, which effectively mitigates decoding errors introduced at wireless relays. In particular, the end-to-end error control problem is modeled as a finite-ring matrix channel problem, for which tight capacity bounds and capacity-approaching schemes are provided. The final part of this dissertation studies the benefit of C&F in random-access wireless networks. In particular, it is shown that C&F significantly improves the network throughput and delay performance of slotted-ALOHA-based random-access protocols.ii Acknowledgements This thesis is the result of the support, help, and advice that I have received from an amazing group of scholars and students at the University of Toronto. Without them this dissertation wouldn't have been possible. First, I feel very fortunate to have two great supervisors: Prof. Frank R. Kschischang and Prof.Baochun Li. As an advisor, Frank has consistently exceeded my expectation. He is not only a brilliant researcher and excellent teacher, but also truly a kind and caring person. He has given me a tremendous amount in the past six years, I can only thank him for a subset. In particular, I have benefited greatly from his focus on fundamental problems, his taste for beautiful mathematics, his emphasis on clarity and grace, and his dedication in developing his students to their full potential. I am very grateful to Frank for making my PhD journey so exciting and rewarding! Frank also has a great sense of humor.I will always remember how much fun we had together during our endless discus...

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“…The proof here extends the proof of [97] by incorporating the physical-layer effect of compute-andforward. The main steps of the proof are the following.…”

Section: Appendix Bmentioning

confidence: 58%

An algebraic approach to physical-layer network coding

Feng

Silva

Kschischang

2010

2010 IEEE International Symposium on Information Theory

132

202

View full text Add to dashboard Cite

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“…In order to accurately characterize the delay in ultradense networks, all aspects should be considered. Such a combination of all these methods, however, is long known to be notoriously difficult [8].…”

Section: Need For New Delay Analysismentioning

confidence: 99%

Toward a Tractable Delay Analysis in Ultra-Dense Networks

et al. 2017

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Meeting the diverse delay requirements of emerging wireless applications is one of the most critical goals for the design of ultradense networks. Though the delay of point-to-point communications has been well investigated using classical queueing theory, the delay of multi-point to multi-point communications, such as in ultradense networks, has not been explored in depth. The main technical difficulty lies in the interacting queues problem, in which the service rate is coupled with the statuses of other queues. In this article, we elaborate on the main challenges in the delay analysis in ultradense networks. Several promising approaches, such as introducing the dominant system and the simplified system, to bypass these difficulties are proposed and summarized to provide useful guidance.

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“…However, according to (5), we find the optimization problem (8) is hardly solvable because µ Φ 0 does not even possess an analytical expression. For that reason, we leverage the dominant system [40], in which every transmitter keeps sending out packets in each time slot (if one transmitter has an empty buffer at any given time slot, it sends out a dummy packet), for an approximation. Since each node is backlogged in the dominant system, that allows us to unpack the interaction amongst queues and derive a closed-form expression for the conditional transmission success probability: Lemma 3: Given stopping set S and conditioned on the spatial realization Φ, the transmission success probability at the typical link under the dominant system is given bŷ…”

Section: A Preliminariesmentioning

confidence: 99%

“…i =j,yi∈S κ 1 + D ji − κ + R 2 \S λκdy 1 + y α /T r α < 1. (40) Now, given a receiver located at the origin, we can rewrite (40) in the following way:…”

Section: Appendixmentioning

confidence: 99%

Optimizing Information Freshness in Wireless Networks: A Stochastic Geometry Approach

Yang

Arafa

Quek

et al. 2021

IEEE Trans. on Mobile Comput.

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Optimization of information freshness in wireless networks has usually been performed based on queueing analysis that captures only the temporal traffic dynamics associated with the transmitters and receivers. However, the effect of interference, which is mainly dominated by the interferers' geographic locations, is not well understood. In this paper, we leverage a spatiotemporal model, which allows one to characterize the age of information (AoI) from a joint queueing-geometry perspective, for the design of a decentralized scheduling policy that exploits local observation to make transmission decisions that minimize the AoI. To quantify the performance, we also derive accurate and tractable expressions for the peak AoI. Numerical results reveal that: i) the packet arrival rate directly affects the service process due to queueing interactions, ii) the proposed scheme can adapt to traffic variations and largely reduce the peak AoI, and iii) the proposed scheme scales well as the network grows in size. This is done by adaptively adjusting the radio access probability at each transmitter to the change of the ambient environment.Index Terms-Poisson bipolar network, age of information, scheduling policy, spatiotemporal analysis, stochastic geometry.

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Asymptotic Stability Region of Slotted Aloha

Cited by 47 publications

References 28 publications

An algebraic approach to physical-layer network coding

An algebraic approach to physical-layer network coding

Toward a Tractable Delay Analysis in Ultra-Dense Networks

Optimizing Information Freshness in Wireless Networks: A Stochastic Geometry Approach

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